Pembrolizumab and Monoclonal Antibody Therapy in Advanced Cancer

Inclusion Criteria: 1. Patient has definitive histologically or cytologically confirmed unresectable or metastatic solid tumor. 2. Patient has one or more tumor measurable as defined by RECIST 1.1 by CT scan (or PET/CT, if patient is allergic to CT contrast media). 3. Patients can be enrolled only on one of the treatment arms on this trial. 4. The investigator will select the appropriate treatment arm for the patient with the following requirements: (a) Patients cannot have had prior progression or intolerance to a specific Mab and then enrolled on an arm with that same Mab plus pembro, (b) The Mab on the arm selected must be considered standard of care or listed in the NCCN guidelines (www.nccn.org) for that cancer type. For Arm 1, patients with HER2 overexpressing MBC eligible for maintenance trastuzumab are allowed after taxane plus trastuzumab plus pertuzumab combination therapy. 5. Have recovered from acute toxicities of prior treatment: 1. \> 3 weeks must have elapsed since receiving any investigational agent. 2. \> 2 weeks must have elapsed since receiving any radiotherapy, or ≥ 3 weeks or 5 half-lives whichever is shorter for treatment with cytotoxic or biologic agents ( ≥ 6 weeks for mitomycin or nitrosoureas). Chronic treatment with non-investigational gonadotropin-releasing hormone analogs or other hormonal or supportive care is permitted. 6. Patient has adequate biological parameters as demonstrated by the following blood counts at time of screening: 7. Absolute neutrophil count (ANC) \> 1500 mm3, platelet count ≥ 100×109 L, hemoglobin ≥ 9 g/dL. 8. Serum creatinine ≤2.0, total bilirubin ≤ 2 mg/dL, AST/ALT ≤ 5 times the upper limit of normal (ULN) range 9. Thyroid stimulating hormone (TSH) within institutional normal limits. If TSH is above the upper limit of normal range, then a free T4 within institutional normal limits is acceptable. 10. Persistent prior systemic therapy non-hematologic AE grade ≥ 2 (except alopecia or correctable electrolyte abnormality with supplementation) 11. Patient has a Karnofsky performance status (KPS) ≥ 70. 12. Women of child-bearing potential (i.e., women who are pre-menopausal or not surgically sterile) must be willing to use an acceptable contraceptive method (abstinence, oral contraceptive or double barrier method) for the duration of the study and for 30 days following the last dose of study drug, and must have a negative urine or serum pregnancy test within 2 weeks prior to beginning treatment on this trial. Inclusion criteria for Phase II only: 1. Patients must have unresectable HER2 overexpressing gastric or GEJ cancers to be enrolled on Cohort 1 of the pembro plus trastuzumab phase II portion. 2. Patients must have HER2 overexpressing MBC to be enrolled on Cohort 2 of the pembro plus trastuzumab phase II portion. 3. Patients must have HER2 overexpressing MBC to be enrolled on pembro plus ado-trastuzumab emtansine phase II portion. 4. Patients must have HNSCC to be enrolled on Cohort 1 of the pembro plus cetuximab phase II portion. 5. Patients must have K-ras, B-raf, N-ras wildtype CRC to be enrolled on Cohort 2 of the pembro plus cetuximab phase II portion. Exclusion Criteria: 1. Active clinically serious infection \> CTCAE (version 4.03) Grade 2. 2. Serious non-healing wound, ulcer, or bone fracture. 3. Patient has known brain metastases, unless previously treated and well-controlled for at least 1 month (defined as clinically stable, no edema, no steroids and stable in 2 scans at least 4 weeks apart). 4. Inability to complete informed consent process and adhere to the protocol treatment plan and follow-up requirements. 5. Patient has known active infection with HIV, hepatitis B, or hepatitis C (patients are NOT required to be tested for the presence of such viruses prior to therapy on this protocol). 6. Requiring daily corticosteroid dose ≥ 10 mg prednisone or equivalent per day. 7. Patient has undergone major surgery, other than diagnostic surgery (e.g., surgery done to obtain a biopsy for diagnosis without removal of an organ), within 4 weeks prior to Day 1 of treatment in this study. 8. Patient has a history of allergy or hypersensitivity to any of the study drugs or any of their excipients, or the patient exhibits any of the events outlined in the Contraindication or Special Warnings and Precautions sections of the product or comparator SmPC or Prescribing Information. 9. Patient has serious medical risk factors involving any of the major organ systems, or serious psychiatric disorders, which could compromise the patient's safety or the study data integrity. 10. Patient will be receiving any other anti-cancer therapy during participation in this trial. 11. Prior treatment with pembro. Receipt of other PD-1 inhibitors or PD-L1 inhibitors is allowed. 12. Active or prior documented autoimmune disease requiring systemic treatment within the past 2 years. Exclusion Criteria for phase II portion only: 1\. Patients with a history of more than one primary cancer, with the exception of: a) curatively resected nonmelanomatous skin cancer; b) curatively treated cervical carcinoma in-situ; or c) other primary solid tumor treated with curative intent and no known active disease present and no treatment administered during the 2 years prior to enrollment.